1.

32a2x3-8b2x3-4a2y3+b2y3.

Answer»

Given \:32a^{2}x^{3} - 8b^{2}x^{3}-4a^{2}y^{3}+b^{2}y^{3} \\= 8x^{3} ( 4a^{2} - b^{2} ) - y^{3}(4a^{2} - b^{2}) \\= (4a^{2} - b^{2})(8x^{3} - y^{3})\\= [(2a)^{2} - b^{2})][ (2x)^{3} - y^{3} ] \\= (2a+b)(2a-b){(2x-y)[(2x)^{2}+(2x)\times b+b^{2}]} \\= (2a+b)(2a-b)(2x-y)(4x^{2}+2bx+b^{2})

THEREFORE.,

\red{32a^{2}x^{3} - 8b^{2}x^{3}-4a^{2}y^{3}+b^{2}y^{3}}\\\green {= (2a+b)(2a-b)(2x-y)(4x^{2}+2bx+b^{2}) }

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